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 Post subject: All possible 3x3x3 - solvingwise
PostPosted: Mon Jun 07, 2010 12:45 pm 
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Joined: Mon Aug 02, 2004 7:03 am
Location: Koblenz, Germany
Hi,
here I come with another finished series and a abstract one too.
All puzzles here have already been published but not collected. The last one arrived yesterday.
Thank you Steryne for helping me finishing this series.
Please take a look at this picture and try to find the system before you look further down.
Attachment:
Loesbarkeiten3x3x3.JPG
Loesbarkeiten3x3x3.JPG [ 343.19 KiB | Viewed 2239 times ]
On a Super3x3x3 you have 5 things to solve:
Permutation of the corners
Orientation of the corners
Permutation of the edges
Orientation of the edges
Orientation of the faces
The ordinary 3x3x3 lacks one of these tasks. Other mods lack other tasks.
Here you see all 18 variants which can be derived from that system.
I defined here that orientation of edges/corners shall not be possible if permutations are invisible.

To wwwmwww:
I can't remember if I wrote to you about this but you should have seen this coming... :lol:


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 Post subject: Re: All possible 3x3x3 - solvingwise
PostPosted: Sat Jun 12, 2010 3:44 pm 
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Joined: Mon Apr 03, 2006 10:38 am
Location: Connecticut
Hi Andreas,

Very nice! I like your exhaustive treatments.

Faces: no contribution (N), or orientation matters (O) - i.e. 2 possibilities
Corners: N, permutation alone matters (P), or permutation and orientation matter (P+O) - i.e. 3 possibilities
Edges: N, P, P+O - i.e. 3 possibilities
total possibilities = 2x3x3 = 18

arrangement in picture:
columns: C:N, C:P, C:P+O
rows: E:N, E:P, E:P+O
in each pair, top is F:O lower is F:N

I have five questions/comments:

F:N|C:P+O|E:N - you use the 2x2x2 but the "corners only" 3x3x3 has also been made (not to mention Oskar's Gerardo's Cube http://twistypuzzles.com/forum/viewtopic.php?f=15&t=16943):
Attachment:
corners-cube.jpg
corners-cube.jpg [ 1.94 KiB | Viewed 2065 times ]


F:O|C:P|E:P - for this one it is tough to see that the corner pieces are different colors - they all look gray

F:O|C:N|E:P+O - this one is an octahedron and I am curious why this goes here - it has the "base" pieces which do not appear in the others - you could apply a coloring to the "simple edges only" that would make center orientations matter:
Attachment:
edges-only-simple1.jpg
edges-only-simple1.jpg [ 2.15 KiB | Viewed 2065 times ]


F:O|C:P|E:P+O - you use the trajber's octahedron, but this is also possible with a 3x3x3 coloration:
Attachment:
8-color-333.jpg
8-color-333.jpg [ 2.34 KiB | Viewed 2065 times ]


Lastly, should the framework be expanded to distinguish between 90/180/270 orientation possibilities on the faces? For example, to encompass the Rubenking:
Attachment:
rubenking.jpg
rubenking.jpg [ 2.26 KiB | Viewed 2065 times ]


Regards,
Rob

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 Post subject: Re: All possible 3x3x3 - solvingwise
PostPosted: Sat Jun 12, 2010 3:50 pm 
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Actually, the Rubenking is not a good example for where only 180 orientations of the faces matter but 90 degree rotations don't... hmmm... is it even possible?

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 Post subject: Re: All possible 3x3x3 - solvingwise
PostPosted: Sat Jun 12, 2010 4:23 pm 
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Rob wrote:
Actually, the Rubenking is not a good example for where only 180 orientations of the faces matter but 90 degree rotations don't... hmmm... is it even possible?

You can, sort of, with the single coloured Fisher Cubes. 4 of the centres can be flipped by 180 degrees and appear no different. :?

Alex

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 Post subject: Re: All possible 3x3x3 - solvingwise
PostPosted: Sun Jun 13, 2010 3:49 pm 
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Joined: Mon Aug 02, 2004 7:03 am
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At least, one comment. Thank you Rob.
You got it perfectly right. I have used a different notation, but this doesn't matter here.
Rob wrote:
F:N|C:P+O|E:N - you use the 2x2x2 but the "corners only" 3x3x3 has also been made (not to mention Oskar's Gerardo's Cube
Oskars invention would suffice too. I (and most other readers) don't own one but almost everybody ownes a 2x2x2.
Rob wrote:
F:O|C:P|E:P - for this one it is tough to see that the corner pieces are different colors - they all look gray
It is hard to see but they are not all gray. They have 4 different colors.
Rob wrote:
F:O|C:N|E:P+O - this one is an octahedron and I am curious why this goes here - it has the "base" pieces which do not appear in the others - you could apply a coloring to the "simple edges only" that would make center orientations matter.
Correct with your last point. A super simple edges only (cool name, btw) would suffice. The octhaedron is the cornerturning one. Cornerturning octahedron is equivalent to faceturning hexahedron. If you ignore the trivial tips you get a puzzle which fits F:O|C:N|E:P+O. Christophs Magic jewel has no trivial tips, means it is more appropriate. I choose this variant because I own it (compared to the magic jewel and another edgesonly cube) and it was massproduced at one point in time.

Rob wrote:
F:O|C:P|E:P+O - you use the trajber's octahedron, but this is also possible with a 3x3x3 coloration
Correct. But again I preferred the Trajbers octahedron because it wass massproduced in the past and is now again.

Rob wrote:
Lastly, should the framework be expanded to distinguish between 90/180/270 orientation possibilities on the faces? For example, to encompass the Rubenking:
Actually, the Rubenking is not a good example for where only 180 orientations of the faces matter but 90 degree rotations don't... hmmm... is it even possible?
They only massproduced example I know of is the monochrome pyramorphix. It would be cool to expand this series. But so far I don't have a single variant of those 9 additional ones.


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 Post subject: Re: All possible 3x3x3 - solvingwise
PostPosted: Mon Jul 26, 2010 11:21 am 
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Joined: Tue Jul 20, 2010 6:26 am
Location: Firenze, Italy
Very interesting.
I like this system.

I made a sticker mod of a 3x3x3 cube that falls nicely in the category
C:P, E:P, F:P.

guzman.


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 Post subject: Re: All possible 3x3x3 - solvingwise
PostPosted: Tue Jul 27, 2010 11:27 am 
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guzman wrote:
I made a sticker mod of a 3x3x3 cube that falls nicely in the category
C:P, E:P, F:P.

And another one with C:O, E:O, F:O
I have ignored those variants intentionally because I don't have variants where these look "natural". But I have some old sticker variations with
C:O, E:-, F:-
C:-, E:O, F:-


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